step11
Error Decay for a Sequence of Adaptive Meshes


step11, a FENICS code which uses the Discontinuous Petrov Galerkin (DPG) method to solve a Poisson problem, and repeatedly refines the mesh, guided by DPG error indicators. Two methods of adaptive refinement are compared, one of which refines cells which represent a fixed percentage of the error (case 0), and one of which refines a fixed percentage of the cells (case1). The problem uses a discontinuous diffusivity function kappa(x,y).

Note that I have installed FENICS using Docker, and so to run this script I issue the commands:

  1. cd $HOME/fenicsproject/step11
  2. fenicsproject run
  3. python3 step11.py
  4. exit

Licensing:

The GNU LGPL license.

Reference:

  1. Jay Gopalakrishnan,
    Five lectures on DPG Methods,
    Spring 2013, Portland State University,
    arXiv:1306.0557v2 [math.NA] 28 Aug 2014.

Source Code:

The error decay plots:

The mesh plots for case 0:

The mesh plots for case 1:


Last revised on 12 November 2018.